Perfect Competition Welfare Outline n n

Perfect Competition & Welfare

Outline n n n Derive aggregate supply function Short and Long run equilibrium Practice problem Consumer and Producer Surplus Dead weight loss Practice problem

n n Focus on profit maximizing behavior of firms Take as given the market demand curve $/unit Equation: P = A - B. Q linear demand n Inverse demand function: willingness to pay Maximum willingness to pay A Constant slope P 1 Demand Q 1 A/B Quantity At price P 1 a consumer will buy quantity Q 1

Perfect Competition n n Firms and consumers are price-takers Firm can sell as much as it likes at the ruling market price q do not need many firms q do need the idea that firms believe that their actions will not affect the market price Therefore, marginal revenue equals price To maximize profit a firm of any type must equate marginal revenue with marginal cost So in perfect competition price equals marginal cost

MR = MC n n n Profit is p(q) = R(q) - C(q) Profit maximization: dp/dq = 0 This implies d. R(q)/dq - d. C(q)/dq = 0 But d. R(q)/dq = marginal revenue d. C(q)/dq = marginal cost So profit maximization implies MR = MC

Perfect competition: an illustration With market price PC $/unit the firm maximizes profit by setting MR (= PC) = MC and producing quantity qc With • The supply curve moves to the right market demand D 2 With Industry supply S 1 and market (a) The Firm (b) Themarket demand D 1 • Price falls and market supply is 1 P 1 equilibrium price S equilibrium price is PC $/unit • Entry continues while profits exist and quantity is Q 1 and quantity is QCthat Now assume • MC Long-run equilibrium is restored Existing firms maximize demand at price Pby increasing profits C and supply curve S 2 S 1 increases to D 1 output to q 1 AC D 2 P 1 S 2 P 1 Excess profits induce PC new firms to enter the market PC qc q 1 Quantity D 2 QC Q 1 Q´C Quantity

Perfect competition: additional points n Derivation of the short-run supply curve q this is the horizontal summation of the individual firms’ marginal cost curves $/unit Example 1: Three firms Firm 3 Firm 1 Firm 2 Firm 1: MCMC/4+ 8 q = = 4 q - 2 q 1+q 2+q 3 Firm 2: MCMC/2+ 8 q = = 2 q - 4 Firm 3: MCMC/6+ 8 q = = 6 q - 4/3 Invert these Aggregate: Q= q 1+q 2+q 3 = 11 MC/12 - 22/3 MC = 12 Q/11 + 8 8 Quantity

Example 2: Eighty firms $/unit Firm i Each firm: MCMC/4+ 8 q = = 4 q - 2 Invert these Aggregate: Q= 80 q = 20 MC - 160 MC = Q/20 + 8 Aggregate 8 Quantity n Definition of normal profit q not the same as zero profit q implies that a firm is making the market return on the assets employed in the business

Practice problem Initial number of firms = 20 1) Find short run equilibrium 2) Find long run equilibrium

Short run

Long run n n P = min avg cost Point at which MC=AC

Efficiency and Surplus n n Can we reallocate resources to make some individuals better off without making others worse off? Need a measure of well-being q q q consumer surplus: difference between the maximum amount a consumer is willing to pay for a unit of a good and the amount actually paid for that unit aggregate consumer surplus is the sum over all units consumed and all consumers producer surplus: difference between the amount a producer receives from the sale of a unit and the amount that unit costs to produce aggregate producer surplus is the sum over all units produced and all producers total surplus = consumer surplus + producer surplus

Efficiency and surplus: illustration The demand curve measures the willingness to pay for each unit Consumer surplus is the area between the demand curve and the equilibrium price The supply curve measures the marginal cost of each unit Producer surplus is the area between the supply curve and the equilibrium price $/unit Competitive Supply PC Aggregate surplus is the sum of consumer surplus and producer surplus The competitive equilibrium is efficient Consumer surplus Equilibrium occurs where supply equals demand: price PC quantity QC Producer surplus Demand QC Quantity

Illustration (cont. ) Assume that a greater quantity QG is traded Price falls to PG $/unit The net effect is a reduction in total surplus Competitive Supply Producer surplus is now a positive part and a negative part PC Consumer surplus increases PG Part of this is a transfer from producers Part offsets the negative producer surplus Demand QC QG Quantity

Output restricted to QM $/unit Suppose output is restricted to QM The market clearing price is PM Consumer surplus is given by this area And producer surplus is given by this area This is the deadweight loss Competitive Supply PM PC There are mutually beneficial trades that do not take place: between QM and QC Demand QM QC MR Quantity

Exercise Consider a competitive industry where all firms are identical with cost function: C = 200 +q 2/2 + 10 q. Market demand is given by: p = 55 -Q/20 Find the long run equilibrium (price, quantity and number of firms. ) • • • Mc=q+10, AC=200/q+q/2+10 Equating get: q/2=200/q q 2 = 400 q=20 p=mc=30 Substituting in demand function: 30=55 -Q/20 Q=500 Number of firms nq=Q n=Q/q=500/20=25

Exercise (continued) Suppose now the government introduces a regulation that limits the size of firms to no more than 10 units. Will there be exit or entry of firms? Find the new long run equilibrium. AC=200/q+q/2+10 AC AC(10)=35 P=35=55 -Q/20 35 30 Q=400 10 20 n=40 q

Exercise (continued) Suppose now the government introduces a regulation that forces firms to produce no less than 40 units. Find the new long run equilibrium. AC=200/q+q/2+10 AC AC(40)=35 P=35=55 -Q/20 35 30 Q=400 20 40 n=10 q

Exercise (continued) Welfare loss: 5*400+100*5/2 Welfare cost: =2, 250 Original Surplus: 55 500*25/2=6, 250 % loss = 36% 35 30 Qs Welfare loss 400 500 Q